The bank said Wednesday it will eliminate overdraft charges for withdrawals of less than $5, reducing the chances of hefty fees for people who make small purchases with debit cards. Under Citizens’ previous policies, customers who bought a $3 cup of coffee with debit cards and inadvertently overdrew accounts could get hit with a $37 charge.

“Customers are very sensitive of overdraft fees,” said John Rosenfeld, the head of everyday banking at Citizens. The bank, he said, was looking for a way to “create more appeal with the mass market, the Average Joe.”

The $5 limit is among several changes to Citizens’ overdraft policies that go into effect Friday. The bank will also begin clearing withdrawals primarily in chronological order, instead of from largest to smallest amount, a practice that generated frequent overdrafts. And the bank will institute a flat $35 charge for every overdrawn transaction and returned check, down from $37.

Citizens, owned by the Royal Bank of Scotland, is the second-largest retail bank by market share in Massachusetts. It settled a $137.5 million class-action lawsuit over its fees last year. Earlier this spring, the bank also agreed to pay fines and restitution of $14 million for what regulators alleged were deceptive practices around its overdraft protection program.

In 2010, concerned that banks were using overdraft protection plans primarily to generate fees, the Federal Reserve changed the regulations so banks could no longer automatically enroll customers in the programs.

For customers who opt out of Citizens’ $30 a year overdraft protection plan, the bank will simply decline the debit transaction or ATM withdrawal if there isn’t enough money in the account.